Geodesic
Rings of Quotients of Rings of Derivations
Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 383-398

Voir la notice de l'article provenant de la source Cambridge University Press

The concept of a rational extension of a Lie module is defined as in the associative case [1, pp. 81 and 79]. It then follows from [3, Theorem 2.3] that any Lie module possesses a maximal rational extension (a rational completion), unique up to isomorphism. If now L and K are Lie rings with L⊆ K, we call K a (Lie) ring of quotients of L if K, considered as a Lie module over L, is a rational extension of the Lie module LL. Although we do not know if for every Lie ring L its rational completion can be given a Lie ring structure extending that of L (as is the case for associative rings), this is so, in any case, for abelian Lie rings (Propositions 2 and 4). 
Kleiner, Israel. Rings of Quotients of Rings of Derivations. Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 383-398. doi: 10.4153/CMB-1968-044-5
@article{10_4153_CMB_1968_044_5,
     author = {Kleiner, Israel},
     title = {Rings of {Quotients} of {Rings} of {Derivations}},
     journal = {Canadian mathematical bulletin},
     pages = {383--398},
     year = {1968},
     volume = {11},
     number = {3},
     doi = {10.4153/CMB-1968-044-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-044-5/}
}
TY  - JOUR
AU  - Kleiner, Israel
TI  - Rings of Quotients of Rings of Derivations
JO  - Canadian mathematical bulletin
PY  - 1968
SP  - 383
EP  - 398
VL  - 11
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-044-5/
DO  - 10.4153/CMB-1968-044-5
ID  - 10_4153_CMB_1968_044_5
ER  - 
%0 Journal Article
%A Kleiner, Israel
%T Rings of Quotients of Rings of Derivations
%J Canadian mathematical bulletin
%D 1968
%P 383-398
%V 11
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-044-5/
%R 10.4153/CMB-1968-044-5
%F 10_4153_CMB_1968_044_5

[1] 1. Findlay, G.D. and Lambek, J., A generalized ring of quotients I, II. Can. Math. Bull. 1 (1958)77-85, 155–167. Google Scholar

[2] 2. Jacobson, N., Lie algebras. Inter science, New York, 1962. Google Scholar

[3] 3. Kleiner, I., Free and injective Lie modules. Can. Math. Bull. 9 (1966) 29-42. Google Scholar

[4] 4. Lambek, J., Lectures on rings and modules. Blaisdell, New York, 1966. Google Scholar

[5] 5. Tewari, K., Complexes over a complete algebra of quotients. Can, J. Math. 19 (1967) 40-57. Google Scholar

[6] 6. Zariski, O. and Samuel, P., Commutative algebra, Vol. I. Van Nostrand, Princeton, 1958. Google Scholar

Cité par Sources :